Dimensionality reduction of multielement glass evidence to calculate likelihood ratios

Abstract

Dimensionality reduction of multivariate elemental concentrations of glass is reported for computing likelihood ratios (LRs). The LRs calculated using principal component analysis (PCA) and a post hoc calibration steps result in very low (<1%) false inclusions when comparing glass samples known to originate from different sources and very low (<1%) false exclusions when comparing glass samples known to originate from the same source. The LRs calculated using the novel PCA approach are compared with previously reported LRs calculated using a more computationally intensive Multivariate Kernel (MVK) model followed by a calibration step using a Pool Adjacent Violators (PAV) algorithm. In both cases, the calibrated LRs limited the magnitude of the misleading evidence, providing only weak to moderate support for the incorrect hypotheses. Most of the different pairs that were found to be falsely included were explained by chemical relatedness (same manufacturer of the glass sources in very close time interval between manufacture). The computation of LRs using dimensionality reduction of elemental concentrations using PCA may transfer to other multivariate data‐generating evidence types.

Forensic glass examinations—A review focused on elemental spectrochemical analysis

“…In a follow‐up study, Gupta et al investigated the use of PCA for dimensionality reduction of multivariate elemental concentrations of glass for computing likelihood ratios and compared it to the multivariate kernel‐PVA calibration previously reported. The PCA‐LR approach resulted in low false exclusion and inclusion rates (<1%) while being less computationally intensive than the MVK‐PVA (Gupta et al, 2021).…”

Improving calibration of forensic glass comparisons by considering uncertainty in feature-based elemental data

“…The BKA typically analyzes the following 18 elements: 7 Li, 23 Na, 25 Mg, 27 Al, 39 K, 42 Ca, 49 Ti, 55 Mn, 57 Fe, 85 Rb, 88 Sr, 90 Zr, 137 Ba, 139 La, 140 Ce,…”

“…The need of more databases to train the models, as it happens in score-based approaches, exacerbates the problem. These data requirements also appear when using principal component analysis (PCA) [27] or other dimensionality reduction techniques.…”

Interpol review of paint, tape, and glass evidence 2019–2022

“…Gupta et al [ 189 ] reported on the use of a novel dimensionality reduction method to calculate likelihood ratios (LRs) from multivariate elemental concentrations of glass using LA-ICP-MS data. The LRs were calculated using principal component analysis (PCA) and post hoc calibration steps resulting in very low (<1%) false inclusions when comparing glass samples known to originate from different sources and very low (<1%) false exclusions when comparing glass samples known to originate from the same source.…”